Contents

A Review of Tax Revenue Forecasting Models for the Scottish
Housing Market

The aim of this report is to provide an overview of different
approaches to modelling the Scottish housing market for the
purposes of tax forecasting. The strengths and weaknesses of each
different modelling approach are assessed against a range of
criteria.

Key findings

Practitioners generally rely on more than one approach for
modelling the housing market in the budget preparations of
national or sub-national governments. Different models are used
for different purposes, such as forecasting, policy costing, and
distributional analysis.

For tax forecasting applications, most practitioners in the
UK and elsewhere rely
on a multivariate model with causal explanatory variables and a
specification based on the long-run relationship between the
costs of renting a house and the costs of owning and occupying a
house. These costs include mortgage interest, maintenance, and
the opportunity cost of alternative financial investments, among
others. These models are also popular in academic research.

The decision to change the current approach and select a
different model or models will depend on the priorities of fiscal
planners and the importance they place on each of the criteria
against which we have reviewed the models.

Background

This technical report was commissioned by the Scottish
Government in response to recommendations by the Scottish Fiscal
Commission to explore the modelling options for forecasting the
Scottish housing market, which in turn is required for forecasting
residential Land and Buildings Transaction Tax (
LBTT)
revenues.
[1] It provides a comparative evidence base for forecasters to
decide whether to change their current approaches, and how to
proceed should they decide to do so. The findings of the report may
also have a more general application in markets other than housing
and for taxes other than
LBTT.

Methodology

To find the alternative approaches, we explored the academic
literature and interviewed professional forecasters in government
departments and central banks in the
UK and elsewhere.

The model classes we evaluated include:

simple rules of thumb, growth accounting models, and external
consensus forecasts that do not require estimated model
parameters (we refer to these as technical assumptions)

time series models that use only the history of housing
prices and transactions themselves (known as univariate time
series models)

behavioural models that use other explanatory economic
variables such as incomes and inflation (known as multivariate
regression models)

collections of multivariate equations that are estimated
simultaneously as a system with few restrictions on how variables
influence each other (known as vector autoregression models)

models that incorporate long-run economic relationships
between housing market variables and predict the path of the
housing market required to maintain these equilibriums (known as
error-correction models)

models that apply a variety of the above techniques within a
national accounting framework for the determination and
projection of gross domestic product (commonly referred to as
large-scale macroeconometric models)

macroeconomic models that use microeconomic foundations and
are estimated as a system (known as dynamic stochastic general
equilibrium models)

models based on either a sample or the entire population of
tax returns or property registrations to model the housing market
(known as microsimulation models).

We assessed the extent to which each model class has been
applied to housing markets for forecasting or policy purposes. If
the model has been widely used for forecasting, we assessed its
likely accuracy over the short- and medium-term budget horizon.

For practical budgeting purposes, forecast model selection may
take into consideration a wide range of qualities beyond accuracy.
We also assessed the following properties of each model class:

Can the model tell a clear story about forecast
revisions?

Does it lend itself to transparent communication with
stakeholders such as parliamentarians, industry groups, and the
public?

Can the model be implemented using data available in
Scotland?

Does it require an appropriate amount of resources to develop
and maintain?

In addition to the formal model assessments, we also looked at
several refinements to the above approaches and complementary
approaches that can be used in parallel to them. These included
Bayesian techniques and dynamic factor modelling, among others.

Findings

The results of our evaluation are summarized in Table S1. The
strengths and weaknesses of each model are compared across
evaluation criteria. Selecting a new approach for the housing
market forecasting framework would need to consider the priorities
of the forecasting body as well as the forecast's role in the wider
budget framework.

If forecasters are concerned only with minimizing forecast
errors, there are many examples of univariate time series, vector
autoregressive, and error-correction models applied to the housing
market in the literature and each would generally be expected to
perform well for the Scottish market. Univariate time series models
are particularly appropriate for the short run-years 1 and 2. For
longer horizons, such as years three to five of the budget outlook,
there is evidence that suggests error-correction models would
perform well.

Policy models (for example, to estimate the impact of budget
measures on house prices, or the impact of consumer behaviour such
as tax forestalling on transactions) call for explanatory variables
in the equation specification with causal interpretation. This
indicates a role for multivariate models, which may or may not
include elements of error-correction models, in preference to a
univariate or vector autoregressive approach.

There are few models or techniques that demonstrated value for
forecasting housing market turning points, the prediction of which
would be particularly useful given the importance of the housing
sector to the wider macroeconomy. There is some evidence that
probit models (that is, models that estimate the probability of an
event occurring-for example a 10 per cent fall in real housing
prices) could be useful for recognizing a peak or a trough. But in
general, predicting structural shifts in the path of the housing
market is difficult and relies on the intuition and judgment of
forecasters and careful monitoring of high-frequency data.

Communicating results in budget publications and before
parliamentary committees generally requires explanatory variables
that represent economic determinants and other structural
influences. Simple structural models that incorporate intuitive
variables with expected signs are best (for example, rising
employment may be expected to increase the volume and price of
residential property transactions). If, however, the priority is to
be transparent and have an independent forecast free of concerns
over political interference, then using a technical assumption
based on an external consensus forecast (that is, an average of a
survey of non-government forecasters) may be useful.

Limitations on the availability of data at a Scotland level for
some variables, while not ruling out any modeling approach, may
impair the performance of some models that have a large number of
parameters to estimate.

Resources would not need to be expanded greatly for most
approaches, if at all. Further, more resource-intensive models may
be justified on the basis of the housing market's importance for
other budget purposes (such as the macroeconomic outlook or for
costing social housing policy).

Finally, we received useful insight from a survey of
UK and international
forecasting practitioners, revealing the following main points:

Most practitioners use a variety of models for different
outcomes (forecasting versus policy costing) or to challenge the
forecast of the main model.

In the
UK, the most commonly
applied model is an error-correction framework based on asset
pricing theory comparing the rental price of housing with the
user cost of owner-occupied housing.

Judgment is important to the forecast, especially in the
early quarters of the forecast period, where monitoring and ad
hoc adjustments of growth rates are often used.

Practitioners do not devote significant resources to
modelling the housing sector in most cases, regardless of the
approach. Teams typically consist of between one and six analysts
working on the housing sector (and in the upper end of this
range, analysts are generally not dedicated to housing on a
full-time basis).